A computer-simulated model of affinity capillary electrophoresis is developed. Unlike existing models, it is able to describe the situation where the concentrations of sample molecules and ligand molecules are commensurable, or even the situation where the zones occupied by these molecules are not mixed initially. The model permits to study the dependence of the spatial and temporal distributions of sample molecules on various parameters such as reaction rate constants, concentrations of sample and reagent, electromigration velocities of sample and reagent and sample injection volume. A collection of peak shapes for different values of parameters is presented. The dependence of peak variance on the ratio of the time of analysis to the characteristic time of reaction is studied.